2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S2 = [0, 1], and the strategy s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c< 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.

At a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred's Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for Wawa's gas is qw=740-400pw + 400ps and the demand for Fred's gas is as = 740-400ps + 400pw. Assume that the marginal cost of each gallon of gasoline is m = $6. The gasoline retailers simultaneously set their prices. What is the Bertrand-Nash equilibrium? The Bertrand-Nash equilibrium is where pw = $ 7.85 and Ps =$7.85. (Enter your responses rounded to two decimal places.) Suppose that for each gallon of gasoline sold, Wawa earns a profit of $1.00 from its sale of salty snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium? The Bertrand-Nash equilibrium is where Pw = $ and Ps = $ (Enter your responses rounded to…

Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers.   Warmbreeze Pricing High Low Flashfry Pricing High 11, 11 2, 15 Low 15, 2 8, 8   For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $15 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. If Flashfry prices high, Warmbreeze will make more profit if it chooses a    price, and if Flashfry prices low, Warmbreeze will make more profit if it chooses a    price.   If Warmbreeze prices high, Flashfry will make more profit if it chooses a    price, and if Warmbreeze prices low, Flashfry will make more profit if…

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